Impedance Calculation and Minimisation for Low Emittance Rings(LERs) T.F. Günzel 3 rd Low Emittance Ring Workshop 8-10 th July Thomas Günzel, III LER

Impedance Calculation and Minimisation for Low Emittance Rings(LERs)

T.F. Günzel3rd Low Emittance Ring Workshop

8-10th July

Thomas Günzel, III LER

Outline:

• Different LERs in comparison• General effects of a smaller beam pipe• Further Impedance relevant properties of LERs• Computations for the MAX-IV 3GeV ring

• cavity tapers• bellows• double flange cavity• BPM buttons

• The risk of Microwave instability• Minimisation respectively optimisation of Impedance• Conclusions


Projects in comparison

• small momentum compaction factor• smaller bunch length• smaller synchrotron frequency

• small emittances• smaller beam sizes

• longer damping times

Smaller beam pipe radius (b)

[1] [2] [3,4,5] [6] [7,8]

LSs come closer to the sub-mm regime in terms of bunch length already studied for FELsThomas Günzel, III LER

Projects in comparison

the Boussard criterion imposes tighter limits on thelong. impedance budget (knowing that it is only indicative)

small beam size and often large circumference makes space charge largerthan the synchrotron frequency for all (here studied) LE-rings.large ratio of space charge to synchrotron can change trans. beam dynamics[9].

The chamber cut-off frequency reaches about 10GHz or more.The search for dangerous trapped modes has to be extended up that frequency.


Effects of a smaller beam pipe(+)

For synchrotron light sources and damping rings which contain many low-gap chambersit reduces the impedance of the tapers:

According to K.Yokoya[10]: L

dbZ

ciZL

20 )(

4)(

and A.Blednykh & S.Krinsky(2010)[11]: dL

bdbcZL

LLL

22

0 2.0arctan

2)/log(

4

2

Long. Impedance of low-gap chambers can be significantly reduced by choosing long tapers

The difference b-d gets smaller, significant reduction of the imaginary part


bb d

L

Effects of a smaller beam pipe(-)

Zlong respectively loss factor κL depend ~b-1 (or b-2) on vert. chamber size

Step regime (Zotter&Kheifets[12])

b

bd

b

dcZL

~ln

4

2 0

Cavity regime according to diffraction model (Zotter&Kheifets[12]):

b

g

LL

1)4/1(

small step (Blednyhk & Krinsky[11])2

1

2

1

LL

bd

b

Slits in a circular chamber (Stupakov [13], Kurennoy[14]):

20 )2()Im(

bcZZ em

L

2

2

4

40

)2(3

2)Re(

bc

ZZ mL

These adverse effects concern above all bellows, absorbers, flanges slits and BPMs.Heatload can become a hot issue!

Long. Resistive wall: 2/3

1~

LL b


Effects of a smaller beam pipe (trans.)

Less steep tapers for low-gap chambers (according to K.Yokoya [10]):

Transverse kicks can deteriorate the vertical emittance (but only in extreme cases)

2/13

1~

Lb

Positive effects:

Negative effects:

Not only with a smaller beam pipe, also with a smaller bunch lengththe kicks get larger!

3

1~b

ZT

bdL

dbZZ

1)(2Im

20

Strong resistive wall:

Depending on ß-fct and pipe material the std vacuum chamber contributes to ßZtotal sensibly

Slits and holes: )cos(420

b

iZZ em

In general: )(32

1~

)(2~

nbn

nZ

b

RZ


Vertical emittance growth due to kicks

This effect has been studied with bunches in sub-mm range for X-FELs. by Dohlus, Zagorodnov, Zagorodnova[15].

11 2'

00

0

cyy

yy y

rmseck

E

eN

y

y

25.02'

kdssksWk rms 5.0)())(( 2

With (CLIC-damping ring):ε0y=1pmß =2mNee=0.66nCk

rms = 1000V/(pCm) (produced by low-gap damping wigglers)this value is quite large, but with a long ID and short bunch possible

<y’2c>0.5 = 2.3·10-7m Δε0y/εy0 5%

Fortunately for the other LER’s it is sensibly smaller.Thomas Günzel, III LER

wiggler

wiggler

Further impedance relevant properties of LERs

In difference to 3rd generation LSs the space inside and betweenthe magnets is very limited which does not allow a large numberof special elements.

Therefore the number of elements (bellows, flanges and vacuum slits etc.) creating high impedance is in general smaller than for existing SRs.

The MAX-IV ring will contain:• 260 flanges• 200 BPMs • 60 bellows in 528m circumference

The existing ESRF SR contains:• 550 flanges• 224 BPMs very modular vacuum system• 290 bellows in 844m circumference


The strongest challenges are the Microwave Instability and heatload.Transverse resistive wall and Head-Tail instability are also important but can be damped with a transverse feedback system or with bunch lengthening via HCavity.

Example:

Simulations (limited to long. Impedance)

• carried out with GdfidL (W. Bruns)[16]• wake field (up to 8m) and subsequent coupling impedance computation (T-

domain)• bunch length 4mm and step size 0.2mm

• eigen mode computation in most cases up to 10.4GHz (F-domain)• computation of the shunt impedance and quality factor of the found

modes by material assignment to different parts of the geometry (some

simplifications applied)The wake field computation was done• to support the eigen mode computation• to provide an input for tracking simulation in long. phase space (MW-instability)

The data is shown in a logarithmic presentation of coupling impedance and the shunt impedance of each mode. The shunt impedance is multiplied by the quantity of the corresponding element in the ring. On top of it the threshold curves for LCBIs are plotted for1) 20ps gaussian bunch, 2) 40ps gaussian bunch and 3) 187ps bunch with HCavity


Both scales (left: coupling impedance and right: shunt impedance) are identical

In order to comply with both requirements is a tremendous amount of computation.

Tapers to low-gap chambers are smoother, but tapers to the cavities not

152mm39.5mm

the cavity was simulated apart (and won’t be shown)

a pipe of 50mm radius was placedbetween the tapers instead.


Cavity taper (MAX-IV)

• many modes at rather high frequency• some already above threshold (20ps gaussian bunch)• as more cavities installed as more dangerous they are

• Q only considers wall dissipation• longer taper reduces shunt impedance• slower damping reduces margin further

upstream taper 39.3mm upstream taper 127mm


Cavity taper (MAX-IV)

4mm bunch4mm bunch

Standard bellows (MAX-IV)


discontinuity in the beam pipe

e- 2b

A

15 elements (there are more of diff. type)the discontinuity has triangular shape

884

33

0

1~

32 bbZR

n

nms

321484 mmAb

kRs 58

According to Kurennoy et al.’s theory [17]of discontinuities:

close to the cut-off at 9.16GHz

Ψ susceptibility

effect of the slits seems to be less important

Rs=167Ω

f=9.07GHz


resonancerather close to the cut-off

For many bellows in the ring such a resonance can become dangerous (in MAX-IV the number is limited though).

Standard bellows (MAX-IV)

Q-value only based onwall dissipationradiation contribution to Q?

4mm bunch

BPM block sandwiched by a double flange (MAX-IV)

resides on each side of the majority of the vacuum chambers (120x)

taper (11->12.5) taper (12.5->11)

absorber protectsBPM block

bellow bellow

bellowbellow

BPM block(w/o buttons)

flangeflange

• taper pair necessary to protect the BPM block from synchrotron radiation• dispose of enough space for the buttons

It is a swallow cavity which allows modes to get trapped


BPM block sandwiched by double flange

f=9.82GHzf=9.34GHz

Rs=3180ΩRs=466Ω


main peak @5.6GHzdouble resonance of in total 98Ω

peak contributes

to MW

4mm bunch

peak contributesto MW

BPM button (MAX-IV)


large shunt impedance Rs = 105Ωbut does not increase heatload

The Power loss is not very high and can, if necessary, be diminished by using Ag- or Au-buttons

no external loadno radiation loss

considered

The small radius of the buttoms leads to a resonance at rather high frequency[18]:

,...2,11

21

mrr

mcf

r

m

4mm bunch

peak contributesto MW

ALBA button in MAX-IVchamber

Rs=370Ω


BPM button (MAX-IV)

no external loadno radiation loss

considered

Due to asymmetric position in rectang. pipe the Rs of the ALBA button is small.In the round MAX-IV chamber there no asymmetry anymore

884

33

0

1~

32 bbZR

n

nms

In case of high Rs and numerous BPMs LCB-instability threshold could be exceeded.However, for small buttons (high freq.resonance) the threshold is high so that the risk is rather limited.

Imagine 250 BPMs with Rs=400 =0.1M

High shunt impedance, what does it mean?

• the material mainly determines the Rs,

• the button radius the peak frequency• it is (R/Q) which enters in

the computation of the MW-instability

Kurennoy’s theory of discontinuities[17]:

The risk of the Microwave instability(MAX-IV)

Despite the long bunches the found MW-threshold is rather close (3.5mA) to the single bunch current 2.84mA MAX-IV made the choice to use high current in long bunches (lengthened by a harmonic cavity).

BPM resonances cannot be avoided.Flange resonances could be short-circuited.


The computation of the Microwave Instability for MAX-IV was presented in the paper of M.Klein, R.Nagaoka, G.Skripka, P.F.Tavares and E.J.Wallen[19].

5.6GHz: resonance in the double flange9.8GHz: resonance in the double flange cavity15.9GHz: resonance in the BPMshowever the resonance of biggest adverse effect is broadband (not shown here)

AeN

IVMAXI epeak 6.10

2)(

However, in several other LER’sthe peak current is even higher.

Minimisation of Impedance


However, the shown examples give some indications:

• For optimisation analytical parametrisation of the impedance is recommended. •The cavity taper shows: use long tapers for cavities and low-gap chambers• By-pass/short-circuit the flanges (NSLS-II [18] and Soleil [20] do it)• Cavities, even rather swallow ones, have to be avoided.• If steps are necessary, make them as soft as possible.• Use well conducting material in order to reduce heatload of BPMs and other sensitive elements• reduce the number of critical elements (less pump slits, bellows, BPMs etc.)• For RW: use of NEG-coated Al or Cu all along the ring

Another approach is to optimise the input parameters of the Boussard criterion:

• choose a moderate peak current (increasing the harmonic number and/or using longer bunches)• tune the RF-system so that it reduces rather the synchrotron tune instead of bunch length• favor machines of higher energy• choose lattices which avoid a rather low momentum compaction factor

The requirements of the mechanical engineering do not allow a large margin for optimisation One of the constraints is to cope with the heatload of the synchrotron radiation Due to the limited space large geometrical variation is anyway not possible. Trans. collective effects benefit from lower β-functions in LER’s compared to existing SRs.

Conclusions

The computation of thresholds and other intensity-related collective effects is by far exact, often the discrepancy between the computed and measured effects is significant.

The key parameter of a resonance Rshunt=(R/Q)·Q depends on Q. It determinesthe threshold of the multi-bunch instabilities. However, the quality factor Q is onlyapproximately known. Q gets contributions from wall dissipation, radiation and possibly external load.

Examples: Transverse impedance budget of Soleil[21] and ESRF[22] is 50-66% of the impedance that was measured.

So far worst case estimations were in most cases sufficient. This will certainly change for LER’s.


Lower β-functions, less special vac.elements and less steep tapers alleviate collective effectsof LERs.

Minimisation of impedance should be done with respect to the most dangerous collective effectSome collective effects can be afforded, others not.

Nevertheless I consider the MW-instability as one of the greatest challenges.

[1]S.Leemann et al.“Beam dynamics and expected performance of Sweden’s new SR LS:MAX-IV”,PRSTAB12 120701(2009)

[2] ESRF Upgrade Programme II (2015-2019), White Paper[3] K.Soutome, LER-workshop 2011 [4]T.Watanabe et al., THPC032, IPAC’11[5] T.Watanabe, talk on the FLS 2010 at SLAC[6] CDR-CLIC CERN-12-007[7] K.Bane et al.”A design report of the baseline for PEP-X”, SLAC-PUB-13999, PUB-14785[8] Y.Cai et al.,”PEP-X, an ultimate storage ring based on 4th order geometric achromats”,SLAC-[9] M.Blaskiewicz,”Fast Head-tail instability with space charge”, PRST-AB 1,044201 (1998)[10] K.Yokoya,”Impedance of slowly tapered structures”,CERN SL/90-88(AP), 1990[11]Blednykh & Krinsky, “Loss factor of short bunches in azimuthally symmetric tapered struct.” PRST-AB 13,064401(2010)

[12]B.Zotter&S.Kheifets,”Impedance and wakes in HE particle accelerators”, World Scientific(98) [13] G.Stupakov, Phys.Rev.E 51,3,(95) 3515[14] S.Kurennoy, Part. Accel. 39,1,(1992) [15] Dohlus et al.,”Impedance of Collimators in the Euro-XFEL”, TESLA-FEL-2010-04, [16] GdfidL, electromagnetic 3D-solver,Warner Bruns, www.gdfidl.de [17] S.Kurennoy et al.,”Coupling impedance of small discontinuities, a general approach”, Phys.Rev.E Vol.52(4),1995

[18] A.Blednykh,”Beam impedance and Heating for several important NSLS-II components”, Miniworkshop,Diamond Jan.13

[19] M.Klein et al.,”Study of collective beam instabilities for MAX-IV 3GeV-ring”, IPAC13[20] R.Nagaoka,”Numerical Evaluation of geometric Impedance for Soleil”, EPAC’04, p.2041[21] R.Nagaoka et al., “Beam Instability Obversations and Analysis at Soleil”, PAC’07[22] T.F.Guenzel, “The transverse coupling impedance of the storage ring at the ESRF”, PRSTAB,9,114402(2006)

References



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Impedance Calculation and Minimisation for Low Emittance Rings(LERs) T.F. Günzel 3 rd Low Emittance Ring Workshop 8-10 th July Thomas Günzel, III LER